On Estimating the Size and Confidence of a Statistical Audit

We consider the problem of statistical sampling for auditing elections, and we develop a remarkably simple and easily-calculated upper bound for the sample size necessary for determining with probability at least c whether a given set of n objects contains b or more “bad” objects. While the size of the optimal sample drawn without replacement can be determined with a computer program, our goal is to derive a highly accurate and simple formula that can be used by election officials equipped with only a simple calculator.